How much can the addition of new features improve the performance?
It depends on the used network as well as the feeding mechanism but let's give an example; 

When working with LSTM, giving the time data (as an integer sequence) in addition to the time-series data(coming from features) dramatically increases the performance of the network. 

[$X_{0}$,$X_{1}$, ...] $\rightarrow$ [[$X_{0}$,$t_{0}$],$[X_{1}$,$t_{1}$], ...]


If you go and look for the kaggle competition winner's notebooks, they do also create additional features based on the featured data.

Let's assume that the performance is already quite high on the three features so that you can predict those three features with high reliability. 
It would only make sense to increase the number of features if you would like to predict additional features!